Finite Group Databasebeta

← #34000406

Subgroups — #34000406

Order 18688.

290 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625828C211yesmaximal, characteristic
2#22625184C211yesmaximal, characteristic
3#22609698C211yesmaximal, characteristic
4#17989607—21no—
5#17989530—21no—
6#17989465—21no—
7#17989465C412yes—
8#17989433C412yescomplemented
9#17989431—21no—
10C2×#14556548C2211yescharacteristic
11C2×#14556503—21no—
12C2×#14556502C411yescharacteristic, complemented
13#17988341—21no—
14C2×C4×C8×C73C411yescharacteristic, complemented
15C2×C22⋊#64408—22no—
16#14556658—41no—
17C22⋊#10596833—22no—
18#14556646—41no—
19(C2×#64408)⋊C4—41no—
20(C2×#64408)⋊C4—41no—
21C22×C4×D73D411yescharacteristic
22C22×#10596831—21no—
23#14556548—41no—
24#14556548—41no—
25C2×#11924007C2×C411yescharacteristic
26C2×#11924007Q811yescharacteristic
27C2×#11924005C2×C411yescharacteristic
28C2×#11924005D411yescharacteristic
29C2×C4×Dic73D411yescharacteristic
30#14556503—24no—
31#14556502—41no—
32C22×C8×C73—21no—
33C2×C42×C73C2×C411yescharacteristic
34C4×C8×C73—41no—
35C22×#64408—42no—
36C2×#10596833—42no—
37C22⋊#64408—42no—
38C22⋊#64408—42no—
39C23×D73C22⋊C411yescharacteristic
40C22×Dic73C22⋊C411yescharacteristic
41C22×Dic73C4⋊C411yescharacteristic
42C22×Dic73C4⋊C411yescharacteristic
43C2×C4×D73—22no—
44C2×C4×D73—21no—
45C2×C4×D73—21no—
46C2×C4×D73—41no—
47C2×#10596831—22no—
48C2×#10596831—41no—
49C2×#10596831—41no—
50#11924007—41no—
51#11924007—41no—
52#11924005—41no—
53#11924005—41no—
54C4×Dic73—21no—
55C4×Dic73—21no—
56C22×C4×C73C4211yescharacteristic
57C22×C4×C73C22⋊C411yescharacteristic
58C22×C4×C73C4⋊C411yescharacteristic
59C2×C8×C73—22no—
60C2×C8×C73—41no—
61C2×C8×C73—41no—
62C42×C73—21no—
63C42×C73—21no—
64C23×C73#9511yescharacteristic
65C22×D73—21no—
66C22×D73—21no—
67C22×D73—41no—
68C22×D73—41no—
69C22×D73#10412yes—
70C2×#64408—82no—
71C2×#64408—82no—
72C2×#64408—82no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73—41no—
78C2×C4×C73—41no—
79C2×C4×C73#9911yescharacteristic
80C2×C4×C73#9911yescharacteristic
81C2×Dic73—21no—
82C2×Dic73—21no—
83C2×Dic73—21no—
84C2×Dic73—21no—
85C2×Dic73—21no—
86C2×Dic73—41no—
87C2×Dic73—41no—
88C4×D73—42no—
89C4×D73—42no—
90#10596833—82no—
91C8×C73—42no—
92#10596831—42no—
93C22×C73—21no—
94C22×C73—21no—
95C22×C73H(3,ℤ/4)11yescharacteristic
96C22×C73#33911yescharacteristic
97C22×C73#34211yescharacteristic
98C2×D73—22no—
99C2×D73—41no—
100C2×D73—41no—
101C2×D73—42no—
102C2×D73—81no—
103#64408—162no—
104C4×C73—21no—
105C4×C73—21no—
106C4×C73—41no—
107C4×C73—41no—
108Dic73—41no—
109Dic73—41no—
110Dic73—41no—
111#7214—731nomaximal, Sylow
112C2×C73—21no—
113C2×C73—21no—
114C2×C73#128411yescharacteristic
115C2×C73#139111yescharacteristic
116C2×C73#139511yescharacteristic
117D73—42no—
118#1820—731no—
119#1750—731no—
120#1464—731no—
121C73#721411yescharacteristic, complemented, Sylow
122C2×#117—731no—
123#432—1461no—
124C2×C22⋊C8—1461no—
125C2×#97—731no—
126C2×C4×C8#6440811yescharacteristic, complemented
127#381—1461no—
128#342—732no—
129#342—1461no—
130#336—1461no—
131#324—732no—
132#323—1461no—
133C23×C4—731no—
134C22×C8—21no—
135C22×C8—1461no—
136#117—2921no—
137#117—2921no—
138C2×C4⋊C4—731no—
139C2×C4⋊C4—731no—
140C2×C22⋊C4—731no—
141C2×C22⋊C4—731no—
142C2×C22⋊C4—1462no—
143C2×C42—731no—
144C2×C42C2×#6440811yescharacteristic
145C4⋊C8—2921no—
146C22⋊C8—1464no—
147C22⋊C8—1462no—
148#97—2921no—
149#97—2921no—
150C4×C8—41no—
151#95—2921no—
152#95—2921no—
153C24—731no—
154C22×C4—2921no—
155C22×C4—2922no—
156C22×C4—731no—
157C22×C4—731no—
158C22×C4—731no—
159C22×C4—1462no—
160C22×C4—1461no—
161C22×C4—1461no—
162C22×C4C4×#6440811yescharacteristic
163C22×C4C22⋊#6440811yescharacteristic
164C22×C4C4⋊#6440811yescharacteristic
165C2×C8—22no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—2921no—
169C2×C8—2921no—
170C2×C8—2922no—
171C2×C8—1462no—
172C4⋊C4—2921no—
173C4⋊C4—2921no—
174C22⋊C4—2921no—
175C22⋊C4—2921no—
176C22⋊C4—2922no—
177C22⋊C4—2922no—
178C42—21no—
179C42—21no—
180C42—1461no—
181C42—1461no—
182C23—2921no—
183C23—2921no—
184C23—732no—
185C23—1461no—
186C23—1461no—
187C23(C2×#64408)⋊C411yescharacteristic
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—2922no—
195C2×C4—2922no—
196C2×C4—2921no—
197C2×C4—2921no—
198C2×C4—5842no—
199C2×C4—5842no—
200C2×C4—5842no—
201C2×C4—1461no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4#1455664911yescharacteristic
207C2×C4#1455665011yescharacteristic
208C8—42no—
209C8—2922no—
210C8—5842no—
211C22—21no—
212C22—21no—
213C22—2922no—
214C22—2921no—
215C22—2921no—
216C22—5841no—
217C22—1462no—
218C22#1798945411yescharacteristic
219C22#1798945811yescharacteristic
220C22#1798946511yescharacteristic
221C4—21no—
222C4—21no—
223C4—41no—
224C4—41no—
225C4—2921no—
226C4—2921no—
227C4—2921no—
228C4—11682no—
229C2—21no—
230C2—21no—
231C2—2922no—
232C2#2262477911yescharacteristic
233C2#2262501911yescharacteristic
234C2#2262503111yescharacteristic
subgroupG/H
centerC22#17989465
commutatorC22×C4×C73C42
FrattiniC2×C42C2×#64408
FittingC2×C4×C8×C73C4
socleC22×C73#342
prime radicalC23×D73C22⋊C4
cosocleC2×#14556548C22
hypercenterC2×C4×C8#64408
hypocenterC73#7214
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
8. #17989433C4semidirect
12. C2×#14556502C4semidirect
14. C2×C4×C8×C73C4semidirect
121. C73#7214semidirect
126. C2×C4×C8#64408semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226258282
#226251842
#226096982
#721473